Using an Expected Loss Function to
Identify Best High Schools for
Recruitment
Sonia M. Bartolomei-Suárez
Associate Dean of Academic Affairs, School of Engineering
David González-Barreto
Professor, Industrial Engineering Department
Antonio González-Quevedo
Professor, Civil Engineering and Surveying Department
University of Puerto Rico, Mayagüez
10/8/2015
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Outline
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Introduction
Objectives
Description of Admission Criteria
Performance of our engineering students in their high
schools
Performance of the students at UPRM’s College of
Engineering
Definition of the Performance Index Using Quadratic Loss
Function
Conclusions
Future Work
References
Acknowledgement
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Introduction
– A study of our entering student profile demonstrates that a large
number of them come from the Western part of the island of
Puerto Rico, our geographic region [1].
– The school of engineering is interested in attracting good students
from all the geographic areas of Puerto Rico.
– With this goal in mind, this study was developed to identify the
best schools in the island, based on the performance of the
engineering students in our university.
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Objectives
– An objective of the strategic plan of the University of
Puerto Rico Mayagüez (UPRM) is to identify and attract
the best possible prospective students from high
schools to the College of Engineering.
– To address this objective a good first step is to identify
the high schools that produce, over a period of years,
the students that better executed within our institution.
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Description of Admission Criteria
– The admission index, which is called the IGS, is composed of the
high school grade point average, the verbal aptitude, and the
mathematics aptitude tests scores from the College Board
Entrance Examination.
– The highest possible value of the IGS is 400.
– The weight of the GPA is 50%, while the weight for each of the two
aptitude tests is 25% each.
– Each academic program determines each year the minimum value
of the IGS.
– In general terms, no other measurement is used to admit a
student in the first year of university studies. For the engineer
class of 2004-2005, the minimum IGS fluctuated from to 313 for
Surveying to 342 for Computer Engineering.
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Performance of our engineering students in their high
schools
– First this study presents the best high schools, private and public,
from the perspective of the student performance in their high
schools.
– The high schools that were included in the study have sent more
than 50 students who have graduated from our School of
Engineering in the past ten years (1995-2005).
– This study was generated using data obtained from the Office of
Institutional Research and Planning of our university.
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Performance of our engineering students in their high
schools
The high schools were analyzed based type of school
(private or public) and:
– The number of graduates that entered at the UPRM’s College
of Engineering during the years 1995-2005 (the top fifteen).
– The average admission index (IGS) for the graduates that
entered at the UPRM’s College of Engineering during the
years 1995-2005 (the top fifteen).
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
CROEM, Mayagüez
397
Patria Latorre, San Sebastian
182
Eugenio María de Hostos, Mayagüez
156
Efrain Sánchez Hidalgo, Moca
149
University Gardens, Río Piedras
146
Blanca Malaret, Sabana Grande
143
Escuelas Públicas
Luis Muñoz Marin, Yauco
140
Miguel Meléndez Muñoz, Cayey
127
Lola Rodríguez de Tió, San Germán
126
Benito Cerezo, Aguadilla
112
Luis Muñoz Marin, Añasco
112
Dr. Carlos González, Aguada
109
Secundaria UPR, Río Piedras
108
Domingo Aponte Collazo, Lares
106
Ramón José Dávila, Coamo
106
0
50
100
150
200
250
300
350
400
Cantidad de Estudiantes
Figure 1. First 15 Public High Schools with 50 or more graduates at
UPRM for the College of Engineering (Years 1995-2005).
450
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Notre Dame High School, Caguas
262
Academia de la Inmaculada Concepción, Mayagüez
182
Colegio San José, Río Piedras
145
Colegio San Ignacio, Río Piedras
122
Academia Discípulos de Cristo, Bayamón
121
Escuelas
Colegio San Antonio, Río Piedras
117
Colegio Marista, Guaynabo
96
American Military, Guaynabo
90
Colegio San Agustín, Cabo Rojo
90
Academia Santa María, Ponce
88
Colegio San Antonio Abad, Humacao
88
Colegio María Auxiliadora, Carolina
87
Colegio San Carlos, Aguadilla
86
Colegio Evagélico Capitán Correa, Arecibo
82
Carvin School, Carolina
77
0
50
100
150
200
250
Cantidad de Estudiantes
Figure 2. First 15 Private High Schools with 50 or more graduates at UPRM
for the College of Engineering (Years 1995-2005).
300
Escuelas Públicas
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Vocacional Antonio Lucchetti, Arecibo
341
Secundaria UPR, Río Piedras
341
Ramón José Dávila, Coamo
340
Leonídes Morales Rodríguez, Lajas
340
Emilio R. Delgado, Corozal
340
University Gardens, Río Piedras
339
Carmen Belén Veiga, Juana Díaz
339
Carmen Bozello de Huyke, Arroyo
338
Eladio Tirado López, Aguada
337
Luis Muñoz Marin, Añasco
337
Patria Latorre, San Sebastían
337
Domingo Aponte Collazo, Lares
337
Juan Quirindongo Morell, Vega Baja
337
Ponce High School, Ponce
336
Asunción Rodríguez, Guayanilla
336
Juan Antonio Corretjer, Ciales
336
333
334
335
336
337
338
339
340
341
IGS
Figure 3. Public High Schools with the highest IGS for graduates
of the School of Engineering within 1995-2005.
342
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Colegio Ponceño
343
Academia San José, Guaynabo
343
342
Escuelas
Colegio San Antonio, Río Piedras
Notre Dame High School, Caguas
340
Colegio San José, Río Piedras
340
Colegio Santo T omás de Aquino, Bayamón
340
Academia de la Inmaculada Concepción, Mayagüez
340
Cupeyville School, Río Piedras
340
Colegio Marista, Guaynabo
340
Carvin School, Carolina
339
Academia Santa María, Ponce
339
Colegio San José, Caguas
339
Colegio Evagélico Capitán Correa, Arecibo
339
Colegio San Antonio Abad, Humacao
339
338
Colegio San Conrado, Ponce
335
336
337
338
339
340
341
342
343
IGS
Figure 4. Private High Schools with the highest IGS for graduates
of the School of Engineering within 1995-2005.
344
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Performance of the students at UPRM’s College
of Engineering
• After identifying the high schools based on the
performance of their students at the high school level, it
was decided to analyze the high schools based on the
performance of their students at the College of
Engineering.
• The high schools were analyzed based on:
- the time to complete a BS in engineering
- the UPRM graduation grade point average (GPA)
- the UPRM graduation rate
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
RIO PIEDRAS-SECUNDARIA UPR
5.59
5.65
CIDRA-ACADEMICA ANA J CANDELAS
COAMO-RAMON JOSE DAVILA
5.79
SAN SEBASTIAN-PATRIA LATORRE
5.79
HUMACAO-ANA ROQUE
5.83
5.87
Escuelas Públicas
ARROYO-CARMEN BOZELLO DE HUYKE
OROCOVIS-JOSE ROJAS CORTES
5.97
CAYEY-MIGUEL MELENDEZ MUNOZ
5.97
JUANA DIAZ-CARMEN BELEN VEIGA
5.97
AGUADILLA-BENITO CEREZO
6.00
LARES-DOMINGO APONTE COLLAZO
6.00
AIBONITO-DR JOSE N. GANDARA
6.03
RIO PIEDRAS-UNIVERSITY GARDENS
6.04
YAUCO-LUIS MUNOZ MARIN
6.09
SAN GERMAN-LOLA RODZ DE TIO
5.30
6.12
5.40
5.50
5.60
5.70
5.80
5.90
6.00
6.10
Tiempo Promedio
Figure 5. Top 15 public high schools with the lowest average time
to complete the bachelor’s degree in engineering (1991-2006).
6.20
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
HUMACAO-COL SAN ANTONIO ABAD
5.48
5.52
PONCE-COL SAN CONRADO
RIO PIEDRAS-COL ESPIRITU SANTO
5.55
Escuelas Privadas
PONCE-COL PONCENO
5.62
CAGUAS-COL SAN JOSE
5.66
RIO PIEDRAS-COL SAN ANTONIO
5.66
AGUADILLA-COL SAN CARLOS
5.67
SAN GERMAN-COL SAN JOSE
5.70
RIO PIEDRAS-COL SAN IGNACIO
5.75
CAGUAS-NOTRE DAME HIGH SCHOOL
5.76
MAYAGUEZ-ACAD LA INMACULADA
5.78
GUAYNABO-COL SAGRADOS CORAZONES
5.80
RIO PIEDRAS-COL SAN JOSE
5.87
CAROLINA-CARVIN SCHOOL
5.88
PONCE-ACAD SANTA MARIA
5.20
5.90
5.30
5.40
5.50
5.60
5.70
5.80
5.90
Tiempo Promedio
Figure 6. Top 15 private high schools with the lowest average time
to complete the bachelor’s degree in engineering (1991-2006).
6.00
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
RIO PIEDRAS-SECUNDARIA UPR
3.22
3.13
SAN GERMAN-LOLA RODZ DE TIO
LARES-DOMINGO APONTE COLLAZO
3.07
COAMO-RAMON JOSE DAVILA
3.06
Escuelas Públicas
SAN SEBASTIAN-PATRIA LATORRE
3.05
MAYAGUEZ-JOSE DE DIEGO
3.05
HUMACAO-ANA ROQUE
3.04
AGUADILLA-BENITO CEREZO
3.04
RIO PIEDRAS-UNIVERSITY GARDENS
3.04
ANASCO-LUIS MUNOZ MARIN
3.04
MAYAGUEZ-CROEM
3.03
CAYEY-MIGUEL MELENDEZ MUNOZ
3.02
SABANA GRANDE-BLANCA MALARET
3.01
AIBONITO-DR JOSE N. GANDARA
3.01
ARROYO-CARMEN BOZELLO DE HUYKE
2.85
3.00
2.90
2.95
3.00
3.05
3.10
3.15
3.20
3.25
GPA Promedio
Figure 7. Top fifteen public schools with highest UPRM Graduation Grade Point Average (GPA)
for students from public high schools who entered the Faculty of Engineering (1991-2006).
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
RIO PIEDRAS-COL ESPIRITU SANTO
3.23
AGUADILLA-COL SAN CARLOS
3.22
MAYAGUEZ-ACAD LA INMACULADA
3.21
PONCE-COL SAN CONRADO
3.21
HUMACAO-COL SAN ANTONIO ABAD
3.20
RIO PIEDRAS-COL SAN ANTONIO
3.19
Escuelas Privadas
SAN GERMAN-COL SAN JOSE
3.15
CAGUAS-COL SAN JOSE
3.12
GUAYNABO-COL SAGRADOS CORAZONES
3.09
CAGUAS-NOTRE DAME HIGH SCHOOL
3.08
CAROLINA-CARVIN SCHOOL
3.07
PONCE-ACAD SANTA MARIA
3.06
ISABELA-COL SAN ANTONIO
3.05
CABO ROJO-COL SAN AGUSTIN
3.04
PONCE-COL PONCENO
3.04
GUAYNABO-AMERICAN MILITARY
3.04
CAROLINA-COL MARIA AUXILIADORA
3.04
2.90
2.95
3.00
3.05
3.10
3.15
3.20
3.25
GPA Promedio
Figure 8. Top seventeen private schools with highest UPRM Graduation Grade Point Average (GPA)
for students from private high schools who entered the Faculty of Engineering (1991-2006).
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
SAN SEBASTIAN-PATRIA LATORRE
83.56
82.46
RIO PIEDRAS-SECUNDARIA UPR
MOCA-EFRAIN SANCHEZ HIDALGO
80.00
Escuelas Públicas
YAUCO-LUIS MUNOZ MARIN
76.06
AGUADILLA-BENITO CEREZO
73.21
COAMO-RAMON JOSE DAVILA
72.73
MAYAGUEZ-EUGENIO M DE HOSTOS
72.09
RIO PIEDRAS-UNIVERSITY GARDENS
71.67
MAYAGUEZ-CROEM
70.59
HUMACAO-ANA ROQUE
70.00
OROCOVIS-JOSE ROJAS CORTES
68.97
CIDRA-ACADEMICA ANA J CANDELAS
68.63
SAN GERMAN-LOLA RODZ DE TIO
68.33
SABANA GRANDE-BLANCA MALARET
65.00
LARES-DOMINGO APONTE COLLAZO
64.91
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
Tasa de Graduación
Figure 9. Top fifteen public high schools with the highest UPRM graduation rates
for students who entered the School of Engineering in the cohorts of 1991-1997.
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
93.02
PONCE-COL SAN CONRADO
MAYAGUEZ-ACAD LA INMACULADA
90.18
PONCE-ACAD SANTA MARIA
82.50
BAYAMON-COL DE LA SALLE
82.22
81.16
CABO ROJO-COL SAN AGUSTIN
Escuelas Privadas
RIO PIEDRAS-COL SAN IGNACIO
80.33
ARECIBO-COL EVANG CAPITAN CORREA
78.05
HUMACAO-COL SAN ANTONIO ABAD
78.05
CAGUAS-NOTRE DAME HIGH SCHOOL
76.26
RIO PIEDRAS-COL SAN ANTONIO
75.56
RIO PIEDRAS-COL SAN JOSE
73.58
68.29
BAYAMON-ACAD DISCIPULOS DE CRISTO
GUAYNABO-AMERICAN MILITARY
66.67
CAROLINA-COL MARIA AUXILIADORA
0.00
58.70
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
100.00
Tasa Graduación
Figure 10. Top fourteen private high schools with the highest UPRM graduation rates
for students who entered the School of Engineering in the cohorts of 1991-1997.
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Performance of the students at
UPRM’s College of Engineering
• Looking at the figures, we realized that the list of
schools that meet the different criteria, were not the
same.
• We saw a need to develop a function that include
all the criteria. This function is based on the
quadratic expected loss function.
• Therefore, these three indicators were combined to
develop a performance index (PI) that will allow
standard ratings of these high schools.
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Definition of the Performance Index Using
Quadratic Loss Function
– The concept of quadratic loss function has been
proposed by Phadke [2] to approximate quality
losses.
– One can develop a performance index (PI) to
compare high schools through the execution of their
students at the high level institutions.
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Definition of the Performance Index Using Quadratic
Loss Function
– The quadratic loss function is given by
Loss(y) = k (y – T)2
(1)
where k is a proportionality constant
and T is the target value for the y characteristic.
– Usually in quality control applications, a tolerance Δ is defined
such that if the y characteristic is within T + Δ (two sided
tolerance) the characteristic is acceptable.
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Definition of the Performance Index Using
Quadratic Loss Function
– The quadratic loss function penalizes the behaviors
that deviate from the target T.
– A challenge with the function is the definition of the
constant k.
– Artiles-León [3] defined this value to assure that the
loss function is not sensitive to the system of units
used to measure the quality characteristic y.
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Definition of the Performance Index Using
Quadratic Loss Function
– For the two sided tolerance problem this definition
becomes:
2
 2 
(2)
k 

 2 
– Using k results in a “standardized” loss function.
Since the standardized version of the loss function
is dimensionless, if several quality characteristics
are considered, their correspondent loss functions
can be added.
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Definition of the Performance Index Using
Quadratic Loss Function
– The quality characteristics or critical indicators that
we are considering are:
• the average time to complete the BS degree
• the average graduation GPA
• the graduation rates for the high schools under
consideration
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Definition of the Performance Index Using Quadratic Loss Function
• These characteristics are not suited for the two sided tolerance
approach.
• The first one, average time to degree, can be described better as an
smaller-the-better characteristic, while the other two average GPA,
and graduation rate of a higher-the-better characteristic form.
• Expanding the standardized concepts to one-sided tolerance
characteristics the following two equations can be derived for smallerthe-better (3) and higher-the-better (4).
SLoss ( y ) 
SLoss ( y ) 
y
2

2

2
y
2
(3)
(4)
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Definition of the Performance Index Using Quadratic Loss Function
• A total standardized loss (TSLoss) for our case study can be defined
as:
2
TSLoss 
y1

2
1
2

y
2
2
3
2
2

2
y3
(5)
where yi, and Δi corresponds to the characteristic and tolerance for
the critical indicators.
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Table 1. Ratings of High Schools Based
on Performance of Index
High School
Performance Index
Colegio San Conrado, Ponce
3.250182
Academia de la Inmaculada Concepción, Mayagüez
3.376351
Secundaria UPR, Río Piedras
3.569336
Colegio San Antonio Abad, Humacao
3.737924
Patria Latorre, San Sebastian
3.74815
Academia Santa María, Ponce
3.796827
Colegio San Antonio, Río Piedras
3.893357
Notre Dame High School, Caguas
3.995966
Ramón José Dávila, Coamo
4.195212
Benito Cerezo, Aguadilla
4.237077
University Gardens, Río Piedras
4.326681
Ana Roque, Humacao
4.376365
Lola Rodríguez de Tió, San Germán
4.440817
Domingo Aponte Collazo, Lares
4.711063
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Conclusions
– Identifying the best high schools in the country allows
us to fulfill our mission of attracting the best possible
prospective students to the College of Engineering.
– This is only a first step in fulfilling our mission. There
are other strategies that we have to develop to enroll
the best students.
– The loss function provides a scientific way to combine
different criterion of performance to identify the best
schools.
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Future Work
– The suggested performance index, based on the TSLoss, should
include additional critical indicators.
– We suggest exploring the following indicators, average GPA in
math courses, average GPA in science courses, average GPA in
language courses, attempted credits, among others.
– A limitation of the described performance index is that it does not
take into account the correlations among the critical indicators
variables considered.
– Techniques such as the Mahalanobis Distance to incorporate such
relationships should be considered.
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
References
[1] González-Barreto, D. and González-Quevedo, A.,“Attracting a More
Diverse Student Population to the School of Engineering of the University
of Puerto Rico at Mayagüez”, Proceedings of the 9th International
Conference on Engineering Education. July 23-28, 2006. San Juan, PR,
pp. R4E21, R4B25.
[2] Phadke, M. S., Quality Engineering using Robust Design, PrenticeHall, Englewood Cliffs, NJ, 1989.
[3] Artiles-León, N., “A Pragmatic Approach to Multiple-Response
Problems using Loss Functions”, Quality Engineering, 9,2, 1996-1997,
pp. 213-220.
Using an Expected Loss Function to Identify Best
High Schools for Recruitment
Acknowledgement
The authors want to acknowledge the assistance
provided by Leo I. Vélez and Irmannette Torres from
the Office of Institutional Research and Planning of
the University of Puerto Rico at Mayagüez for
providing and validating the data used in this study.
Using an Expected Loss Function to Identify Best
High Schools for Recruitment